With any content changes you should expect some shift, Google can sometimes put you in a dance which can seem your rankings worsen only to improve the next coming weeks to months hence they call this the Google dance.
Off Page SEO
Nowadays content changes have less of an impact than off page SEO so you should consider that this could just of happened for other reasons other than the changes done on the site, Bing however could be reacting to the changes while Google may just be dancing you around for other reasons.
As long as you haven't over optimized then you should see improvement, if you have over optimized then you should expect a drop in rankings... There's lots of threads on the internet about over-optimization. But again, with Google must changes in rankings is off page SEO (links, social media mentions, citations, and so on... content is king is true but only when people see and talk about your content).
Never Under Estimate the Power of Bing
In my line of work I often hear my customers say I don't care about Bing no one uses it... just as you mentioned in your question. Never under estimate the power of Bing, in fact for some niches more people use Bing than Google. Bing current holds a market share of around 30% while Google 66%, by 2016 it is expected that Bing will hold 40% of the market share and Google drop to around 58%. Currently there is over 500 million people using Bing daily for their searches to consider them unworthy is bad for business and Bing should be just as important as Google.
It's important to note that I said that some people in some niches use Bing more than Google, this is true for example Xbox uses Bing, so generally console searchers are younger and will generally visit game sites so this changes the share hold, some users like older people use bing because most often they use Bing because its either preloaded on their machine or its the top one to pick when picking the default, many variables involved but you get my drift, bottom line is Bing is important and will be more important as we approach 2016 and later.